How to solve -0.7(x)^(2)+1=0

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve -0.7(x)^(2)+1=0 | Equatix

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Question

$$-0.7 { x }^{ 2 } +1=0$$

Solve for x

$x = \frac{\sqrt{70}}{7} \approx 1.195228609$
$x = -\frac{\sqrt{70}}{7} \approx -1.195228609$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Subtract $1$ from both sides. Anything subtracted from zero gives its negation.

$$-0.7x^{2}=-1$$

Divide both sides by $-0.7$.

$$x^{2}=\frac{-1}{-0.7}$$

Expand $\frac{-1}{-0.7}$ by multiplying both numerator and the denominator by $10$.

$$x^{2}=\frac{-10}{-7}$$

Fraction $\frac{-10}{-7}$ can be simplified to $\frac{10}{7}$ by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{10}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{70}}{7}$$ $$x=-\frac{\sqrt{70}}{7}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an $x^{2}$ term but no $x$ term, can still be solved using the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$, once they are put in standard form: $ax^{2}+bx+c=0$.

$$-0.7x^{2}+1=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $-0.7$ for $a$, $0$ for $b$, and $1$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-0.7\right)}}{2\left(-0.7\right)}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-0.7\right)}}{2\left(-0.7\right)}$$

Multiply $-4$ times $-0.7$.

$$x=\frac{0±\sqrt{2.8}}{2\left(-0.7\right)}$$

Take the square root of $2.8$.

$$x=\frac{0±\frac{\sqrt{70}}{5}}{2\left(-0.7\right)}$$

Multiply $2$ times $-0.7$.

$$x=\frac{0±\frac{\sqrt{70}}{5}}{-1.4}$$

Now solve the equation $x=\frac{0±\frac{\sqrt{70}}{5}}{-1.4}$ when $±$ is plus.

$$x=-\frac{\sqrt{70}}{7}$$

Now solve the equation $x=\frac{0±\frac{\sqrt{70}}{5}}{-1.4}$ when $±$ is minus.

$$x=\frac{\sqrt{70}}{7}$$

The equation is now solved.

$$x=-\frac{\sqrt{70}}{7}$$ $$x=\frac{\sqrt{70}}{7}$$

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Example

Question

Solve for x

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula